AFFINE LAUMON SPACES AND A CONJECTURE OF KUZNETSOV

We prove a conjecture of Kuznetsov stating that the equivariant K-theory of affine Laumon spaces is the universal Verma module of the quantum affine algebra of Uq.gPln/. We do so by reinterpreting the well-known action of the quantum toroidal algebra of type Uq;q.gRln/ on the K-theory of affine Laumon spaces in terms of the shuffle algebra, which allows us to use a certain embedding of the quantum affine algebra into the quantum toroidal algebra.

Automated summary

This article proves a conjecture about the equivariant K-theory of affine Laumon spaces and establishes a connection between the quantum affine algebra and the quantum toroidal algebra by reinterpreting the action of the latter on the K-theory in terms of the shuffle algebra.